What is the derivative of 4xsin(xcos(x)) ?

The derivative of 4xsin(xcos(x)) is 4(sin(x)cos(x)+xcos(2x))

What is the first derivative of 4xsin(xcos(x)) ?

The first derivative of 4xsin(xcos(x)) is 4(sin(x)cos(x)+xcos(2x))

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\frac{d}{d x} (4 x sin (x) cos (x))

4 (sin (x) cos (x) + x cos (2 x))

Solution steps

\frac{d}{d x} (4 x sin (x) cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x sin (x) cos (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (x) cos (x)

= 4 (\frac{d x}{d x} sin (x) cos (x) + \frac{d}{d x} (sin (x) cos (x)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (x) cos (x)) = cos (2 x)

= 4 (1 \cdot sin (x) cos (x) + cos (2 x) x)

Simplify

= 4 (sin (x) cos (x) + x cos (2 x))

\frac{d y}{d x} = 7 x^{2} - x y

\frac{\partial}{\partial x} (e^{- 8 y} cos (π x))

x^{3} - 3 x + 1 (3.19)

\int tan^{8} (x) sec^{2} (x) d x

x y^{^{'}} = - y - x, y (1) = 1

What is the derivative of 4xsin(xcos(x)) ?
The derivative of 4xsin(xcos(x)) is 4(sin(x)cos(x)+xcos(2x))
What is the first derivative of 4xsin(xcos(x)) ?
The first derivative of 4xsin(xcos(x)) is 4(sin(x)cos(x)+xcos(2x))